Such a filling device is known from DE 20 105 716 U1. The known filling device is embodied in the form of a filler carousel comprising a carrier rotating about a vertical axis of revolution at the outer periphery of which a plurality of filling valves are disposed, which are arranged above supports for packages, such as for example bottles, and fill them with a product. The filling valves are supplied with the product via a store tank located on the carrier of the carousel and rotating along with it about the axis of revolution. The filling device furthermore contains a product circuit which permits, for example in case of a standstill of the machine, to circulate the product that cannot be filled into the packages until filling is possible again. A heat exchanger for the product is arranged in this product circuit which prevents the product from cooling in case of hot filling of the product. Such filling devices must be cleaned and sterilized at the latest when a product is changed. This is accomplished e.g. by steam and/or hot water. If the same is passed through the plant, the plant parts connected thereto are heated. As it is often not desired or even harmful for the product to come into contact with the plant parts heated to sterilization temperature, the complete filling device has to cool down before it is put into operation again. Thereby, time required for sterilizing during which a filling and package plant, of which the filling device is a component, is also forced to a standstill, is increased. In such a plant, further machines for the container manufacture and container treatment (stretch blow machines, sterilizing apparatuses, rinsers, etc.) can be provided upstream of the filling device with respect to the container transport direction, and container treatment machines, such as seamers, inspection machines, labeling machines, transporters, packing and palletizing machines, can be provided downstream thereof.